On Nov 1, 5:50 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
> On 11/1/07, Utpal Sarkar <[EMAIL PROTECTED]> wrote:
>
> > 1) Does anyone know if sage has functions that compute the fixed field
> > for a given subgroup of the Galois group?
>
> Short answer -- no, not yet.
> Just out of curiosity, do you want to do this in a setting where the
> computation is very difficult? Or just sort of routine small computations?
> E.g., could you give an example of the field, etc.?
For the moment I just need it for some easy case in which it can be
done by hand easily, namely the fixed field under an involution of a
number field. It was more out of curiosity and for possible later use.
>
> > 2) Is there a function to obtain the Artin map of an Abelian
> > extension, or at least for the Hilbert class field of a quadratic
> > field?
>
> Maybe PARI (included in SAge) can do some of this. I don't think
> Sage itself has an easy interface to this functionality yet.
>
> William
Ok, thanks!
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